论文标题
引力偶极子上的太阳系限制
Solar System limits on gravitational dipoles
论文作者
论文摘要
Hadjukovic（2010）的引力偶极理论是基于以下假设：反物质具有负重力质量，因此在地球上落在地球上。从天体物理上讲，该模型与修改后的牛顿动力学（MOND）相似，但更基本的模型，其中牛顿重力$ g _ {_ n} $ to syport $ g $ n = 1 + \ lest（α/x \ right）\ tanh \ tanh \ tanh \ sqrt（\ sqrt） g _ {_ n}/a _ {_ 0} $和$ a _ {_ 0} = 1.2 \ times 10^{ - 10} $ m/s $^2 $是mond加速常数。我们表明，$α$必须位于$ {0.4-1} $的范围内，以适合Galaxy旋转曲线。在太阳系中，此插值功能意味着$ {αa_ {_ 0}} $的额外的日落加速度。这将导致土星在15年内从已知的初始位置和近圆形轨道上的速度开始，从而使土星偏离牛顿期望的$ {7000 \ left（α/0.4 \ right）} $ km。我们证明，由于每个行星的重力在太阳上占主导地位的区域，其他行星的假定偶极子光环不应显着改变这一预测。土星的轨道应类似地受到外部太阳系中可能的第九行星和银河系重力的影响，从而导致重力偶极子的非球形分布，从太阳产生了几种kau。 Cassini航天器的无线电跟踪轨道土星产生了$ {5σ} $的上限，即与其常规计算的轨迹的偏差相对于其传统计算的轨迹的上限。这些测量值意味着$α$的上限比与旋转曲线数据一致性所需的最小值要严格得多。因此，$α$的值不可能同时匹配所有可用的约束，从而以极高的意义伪造了其当前形式的重力偶极理论。
The gravitational dipole theory of Hadjukovic (2010) is based on the hypothesis that antimatter has a negative gravitational mass and thus falls upwards on Earth. Astrophysically, the model is similar to but more fundamental than Modified Newtonian Dynamics (MOND), with the Newtonian gravity $g_{_N}$ towards an isolated point mass boosted by the factor $ν= 1 + \left( α/x \right) \tanh \left( \sqrt{x}/α\right)$, where $x \equiv g_{_N}/a_{_0}$ and $a_{_0} = 1.2 \times 10^{-10}$ m/s$^2$ is the MOND acceleration constant. We show that $α$ must lie in the range ${0.4-1}$ to acceptably fit galaxy rotation curves. In the Solar System, this interpolating function implies an extra Sunwards acceleration of ${αa_{_0}}$. This would cause Saturn to deviate from Newtonian expectations by ${7000 \left( α/0.4 \right)}$ km over 15 years, starting from known initial position and velocity on a near-circular orbit. We demonstrate that this prediction should not be significantly altered by the postulated dipole haloes of other planets due to the rather small region in which each planet's gravity dominates over that of the Sun. The orbit of Saturn should similarly be little affected by a possible ninth planet in the outer Solar System and by the Galactic gravity causing a non-spherical distribution of gravitational dipoles several kAU from the Sun. Radio tracking of the Cassini spacecraft orbiting Saturn yields a ${5σ}$ upper limit of 160 metres on deviations from its conventionally calculated trajectory. These measurements imply a much more stringent upper limit on $α$ than the minimum required for consistency with rotation curve data. Therefore, no value of $α$ can simultaneously match all available constraints, falsifying the gravitational dipole theory in its current form at extremely high significance.
